Supply Function Equilibria of Pay-as-Bid Auctions
IFN Working Paper No. 787
31 Pages Posted: 24 Sep 2010
Date Written: December 31, 2008
Abstract
This paper characterizes the Nash equilibrium in a pay-as-bid (discriminatory), divisible-good, procurement auction. Demand by the auctioneer is uncertain as in the supply function equilibrium model. A closed form expression is derived. Existence of an equilibrium is ensured if the hazard rate of the perfectly inelastic demand is monotonically decreasing and sellers have non-decreasing marginal costs. Multiple equilibria can be ruled out for markets, for which the auctioneer’s demand exceeds suppliers’ capacity with a positive probability. The derived equilibrium can be used to model strategic bidding behaviour in pay-as-bid electricity auctions, such as the balancing mechanism of United Kingdom. Offer curves and mark-ups of the derived equilibrium are compared to results for the SFE of a uniform-price auction.
Keywords: supply function equilibrium, pay-as-bid auction, discriminatory auction, divisible good auction, oligopoly, electricity market
JEL Classification: C62, D43, D44, L11, L13, L94
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